bayeisan_modelling.ipynb

{
 "metadata": {
  "name": "Untitled0"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## Logistic Function"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%matplotlib inline\nimport numpy as np\nimport matplotlib.pyplot as plt\n\ndef logistic(x, a):\n    return 1 / (1 + np.exp(-a * (x - 5)))\n\nplt.figure(figsize=(14,4))\nx = np.linspace(0, 10, 1000)\n\nplt.subplot(1, 2, 1)\nplt.plot(x, logistic(x, 1))\nplt.xlim((0,10))\nplt.xlabel('x')\nplt.ylabel('f(x)')\nplt.title('a = 1')\n\nplt.subplot(1, 2, 2)\nplt.plot(x, logistic(x, 2))\nplt.xlim((0,10))\nplt.xlabel('x')\nplt.ylabel('f(x)')\nplt.title('a = 2')\nplt.show()",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA0IAAAEZCAYAAAC6iJVpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XlY1WX+//EXKplm7itLouKCO4maWQ1WLtlEjVphmuUW\n5q91mqamplGbvqVZ0yJOaYvmElpZaWlYmLiGmJpmaq4Y4pJm5L4A5/fHPWIkR0HO4T7nfJ6P6zoX\noEd9+bn0fvP+3PfnvoNcLpdLAAAAAOAgZWwHAAAAAIDSRiMEAAAAwHFohAAAAAA4Do0QAAAAAMeh\nEQIAAADgODRCAAAAAByHRggAAACA49AIAT5m4cKF6tKli6pWraoGDRrYjgMAQAFjx45Vq1atVLly\nZTVs2FAvvfSS7UjARaERAnxMpUqVNGTIEI0dO9Z2FAAACjV16lRlZ2crOTlZiYmJmjlzpu1IQLHR\nCAHFMHr0aEVGRqpy5cpq0aKFPv30U4//Ge3bt1e/fv2YDQIAFFtp1KnHH39cbdu2VZkyZdSkSRPd\neuutWrZsmcf/HMDbaISAYoiMjNTSpUt16NAhjRgxQv3799fevXsLfe/777+vatWqFfqqXr26du3a\nVcrpAQCBrrTrlMvl0uLFi9WyZUtP/1UArwtyuVwu2yEAfxUdHa1Ro0YpLi7O4793SkqKhg4dqh07\ndnj89wYAOIM365QkjRgxQnPmzFF6erqCg4O98mcA3sKMEFAMU6ZMUXR0dP4ds/Xr1+uXX36xHQsA\nAEmlW6cSExM1bdo0zZ07lyYIfolGCCiinTt36r777tP48eN18OBB/frrr2rZsqXcTapOnz5dl19+\neaGvypUrszQOAOBRpVmn3n33Xb344otasGCBQkJCvPVXAryqnO0AgL84evSogoKCVLNmTeXl5WnK\nlClav3692/f369dP/fr1K/af43K5dPLkSZ0+fTr/86CgIF1yySUliQ8ACHClVaemT5+up59+WgsX\nLlREREQJEgN2MSMEFFHz5s312GOPqVOnTqpbt67Wr1+va665xuN/zqJFi1SxYkXdfPPNyszMVIUK\nFdSjRw+P/zkAgMBSWnXqmWee0cGDB9W+ffv8GaThw4d7/M8BvM2rmyUMGjRIc+fOVe3atfX9998X\n+p6HHnpIX3zxhSpWrKjJkycrOjraW3EAACiAOgUAzuXVGaGBAwcqOTnZ7c/PmzdPW7du1ZYtWzRx\n4kTdf//93owDAEAB1CkAcC6vNkLXXnutqlWr5vbn58yZo3vuuUeS1LFjR2VnZ2vfvn3ejAQAQD7q\nFAA4l9VnhLKyshQeHp7/dVhYGDtpAQB8BnUKAAKX9c0S/viIUlBQkKUkAACcizoFAIHJ6vbZoaGh\nyszMzP96165dCg0NPed9kZGR2rZtW2lGAwD8QaNGjbR161bbMUoVdQoA/Edx65TVRiguLk6JiYmK\nj49XWlqaqlatqjp16pzzvm3btrk9DMzpRo4cqZEjR9qO4ZO4Nu5xbdzz52uTmyv98ou0f795/fqr\nlJ1tXhf6/PhxqUIFqVIl87r88rOfn3lNnuy8mRDqVMn58/8pb+PauOcP1+bUKSkjQ9q6Vdq2zXzc\nulXKzJR275YOH5bq1pVCQqR69aQ6daTq1Qt/Va1qxtnLLpPKXeC7c3+4NrYUd8beq41Q3759tWjR\nIh04cEDh4eEaNWqUTp8+LUlKSEhQz549NW/ePEVGRuqyyy7TpEmTvBkHAPyOy2Wam127pKws83Hf\nPunnn81r//6zn2dnm2Jau7ZUs6ZUrZp5Va1qXpGRZz///Y9XrWqKb5kLLJaePLlU/sqlijoFoCj2\n75dWrZLWrpXWrTMft22TQkPN2Nqokfl4ww1S/fqm+alR48LjKuzyaiOUlJR0wfckJiZ6MwIA+LTT\np6WdO01B3b5d2rGjYNOze7eZqQkLMwU3NNTcWWzaVLrmGtP01K4t1apliu6F7iSiIOoUgD9yuczM\nzpIl0tKl0rJl5gZUu3ZSmzZSt27S449LUVFS+fK206IkKJl+LjY21nYEn8W1cY9r4543rk1urlk+\n8cMP0saNZ5uebdtMoxMSYu4mNmokRURIrVubhudM81OxoscjAaWG8cY9ro17pX1tTpyQUlOlefPM\n6/hxKTZW6txZeuQRqUULqWzZUo3kFv9uPCfI5QeLmoOCglh7DcDnuVxmdmfNGmnDhrOvH380szbN\nm5s7iGeWUTRsaJZQBAfbTl40jMXucW0A/5OTIy1YIE2fLs2ZI7VqJfXsaV6tW0tsEOl/ijsW0wgB\nwEVwucyMzurVZt346tXmdemlUtu2UsuW5g5i8+ZSs2bmIVh/x1jsHtcG8B87d0pvvGGee7ziCqlf\nP+nOO83GBvBvNEIA4AUnTkgrV5q14suWScuXmw0G2rUzryuvNK9ALqSMxe5xbQDft2SJ9J//SIsX\nSwMGSMOGmectEThohADAA06cMA3PV1+Zorl2rZnd6dzZbFLQubPZtMBJGIvd49oAvmvxYmnkSDMT\n9Pe/S/37mxtZCDw0QgBwEVwu6fvvpS+/NM3P8uVmaVvXruaB2Y4dA2N5W0kwFrvHtQF8z/r10qOP\nmt04//lPswTOX57JxMWhEQKAIjp9Wlq0SPr0U/OgbHCw2Ra1a1epSxdz1g7OYix2j2sD+I6DB6UR\nI6SZM83HhASOFnCK4o7F/LMA4CgnTkhz50offyx98YXUpIl0663S/PlmUwN2CQIA/zVnjnn259Zb\nzXEFNWrYTgRfxowQgICXm2vOh5g+3cz+REdLt98uxcWZM3xQNIzF7nFtALuys6WHHzYHoE6aJF13\nne1EsIEZIQD4n40bpbfflpKSzMYGd90l/fvf5pBSAEBg+O47qU8fs7R53To2QkDR0QgBCCgnTkiz\nZkkTJ0qbN0v33msOzIuKsp0MAOBpkydLjz8ujRsnxcfbTgN/QyMEICDs3GkK4XvvmaVvDz5o1oiz\nQxAABJ68PLMV9mefmaXPLVrYTgR/RCMEwK99+6308stm2+t775W++UaKjLSdCgDgLSdPSvfcI+3e\nbcb86tVtJ4K/KmM7AAAUl8slJSeb83169ZJiYqTt201DRBMEAIHr8GGpRw+zCc6XX9IEoWSYEQLg\nN1wuU/hGjDDF8KmnpDvuYPkbADjBmSaoZUvpv/+Vypa1nQj+jkYIgM9zuaSUFNMAZWebj7ffLpVh\nThsAHOHwYemmm8yzQG+8wfgPz+AcIQA+be1a6bHHpMxMaeRIMwPEXUA7GIvd49oA3nPqlGmCGjQw\nO4LSBMGd4o7F/FMC4JN275YGDzbnQvTqJa1fL/XtSxMEAE6SlycNHChVqSJNmEATBM/inxMAn3Li\nhDn0tFUrqWZNcxbQ8OE8BwQATvSPf0gZGdL06dwIg+fxjBAAn5GSYpqeFi2kVaukiAjbiQAAtrz3\nnvTJJ2aL7AoVbKdBIOIZIQDW7d1rngNatswcinrLLbYToTCMxe5xbQDPWrXK7BC3aJHUvLntNPAX\nPCMEwG+4XNKUKVLr1lJ4uPTDDzRBAOB0+/ebZ0PffJMmCN7F0jgAVuzdKyUkSDt2SPPnS9HRthMB\nAGzLy5PuvttsjtO7t+00CHTMCAEodTNnSm3amEPxVq6kCQIAGK+/bs6L+/e/bSeBEzAjBKDUHD5s\nNkP49lvps8+kDh1sJwIA+Ip166T/+z8pLY2dQlE6mBECUCq++06KiZHKlzcPwdIEAQDOOHFCuusu\n6eWXpUaNbKeBU9AIAfAql0saP17q2lUaMUJ6+22pYkXbqQAAvuS556QmTczzQUBpYWkcAK85elQa\nNEjaskVavlxq3Nh2IgCAr1m3TpowQVq7VgoKsp0GTsKMEACv2L5d6tTJHIJHEwQAKExOjjR4sPTC\nC1JIiO00cBoaIQAel5JimqChQ6VJk6RLL7WdCADgi8aNky6/3DRDQGkLcvnBUdic2A34B5dLevVV\n6cUXpaQkKTbWdiJ4EmOxe1wboPj27jXHKCxbJjVtajsNAkFxx2KeEQLgEbm50sMPS4sWma1P69e3\nnQgA4MueekoaOJAmCPbQCAEosaNHzSngx45JS5dKVarYTgQA8GXp6VJysrRpk+0kcDKeEQJQIvv2\nSV26SNWrS/Pm0QQBAM4vL0968EGzQULlyrbTwMlohABctK1bpauvlnr2NJsiXHKJ7UQAAF83a5bZ\nLY4zg2AbmyUAuCjr10vdu0v/+peUkGA7DUoDY7F7XBugaHJypBYtpMREc9A24EnFHYu9OiOUnJys\nZs2aqXHjxhozZsw5P3/gwAH16NFDbdu2VcuWLTV58mRvxgHgId9+K914o/TSSzRB8G/UKaB0TZ4s\nhYWZGgLY5rUZodzcXDVt2lQpKSkKDQ1V+/btlZSUpKioqPz3jBw5UidPntQLL7ygAwcOqGnTptq3\nb5/KlSu4hwN32gDfsXix1KeP9PbbUlyc7TQoTYE2FlOngNJ1/LjUpIlZGtehg+00CEQ+MyOUnp6u\nyMhIRUREKDg4WPHx8Zo9e3aB99SrV0+HDh2SJB06dEg1atQ4p7gA8B1ffWWaoKQkmiD4P+oUULrG\nj5fat6cJgu/w2mielZWl8PDw/K/DwsK0YsWKAu8ZOnSorr/+eoWEhOjw4cP64IMPvBUHQAl9/bXU\nr5/0ySdS58620wAlR50CSs/Ro9LYsdLChbaTAGd5rREKCgq64Huef/55tW3bVqmpqdq2bZu6du2q\ntWvX6vLLLz/nvSNHjsz/PDY2VrEcWQ+UmkWLpPh46aOPaIKcJDU1VampqbZjeA11Cig9EyZIf/qT\n1Ly57SQIJCWtU15rhEJDQ5WZmZn/dWZmpsLCwgq8Z/ny5Xr66aclSY0aNVKDBg30448/KiYm5pzf\n7/cFBkDpWbpUuv12aeZM6brrbKdBafrjN/OjRo2yF8YLqFNA6ThxQnr5ZWnuXNtJEGhKWqe89oxQ\nTEyMtmzZooyMDJ06dUozZ85U3B8eKmjWrJlSUlIkSfv27dOPP/6ohg0beisSgGL65hupVy/p/ffN\noalAIKFOAaVj0iQpOlpq29Z2EqAgr80IlStXTomJierevbtyc3M1ePBgRUVFacKECZKkhIQEPfXU\nUxo4cKDatGmjvLw8vfjii6pevbq3IgEohu+/l267TZoyhW1OEZioU4D3nT4tvfiiuaEG+BoOVAVw\njowM6ZprzFKGO++0nQa+grHYPa4NULj33jM31BYssJ0ETlDcsZg9QAEU8PPPUrdu0pNP0gQBAC6e\ny2Vmg157zXYSoHBee0YIgP85dEi66Sapb1/pgQdspwEA+LOvvpLKlZNuuMF2EqBwLI0DIEk6eVLq\n2dOc+v3f/0pF2FkYDsNY7B7XBjjXTTdJd9whDRxoOwmcorhjMY0QALlc0oAB0rFj0gcfSGXL2k4E\nX8RY7B7XBiho40az22hGhnTppbbTwCl4RghAsT37rLR5s5SaShMEACi5V1+V7r+fJgi+jUYIcLjp\n080ZD2lpUoUKttMAAPzdgQNmdcGmTbaTAOdHIwQ42NKl0qOPSl9/LdWtazsNACAQvPWW9Je/SHXq\n2E4CnB+NEOBQW7dKffpIU6dKLVvaTgMACAS5udKECdKsWbaTABfG9tmAA/32m/TnP0sjRkjdu9tO\nAwAIFPPnS7VqSe3a2U4CXBiNEOAweXlS//7mXIf777edBgAQSN58Uxo2zHYKoGjYPhtwmH/9y+wO\nl5IiXXKJ7TTwJ4zF7nFtACkzU2rbVvrpJ+myy2yngROxfTYAtz75RJo8WVq5kiYIAOBZb78t9e1L\nEwT/wYwQ4BAbNkh/+pM0b57Uvr3tNPBHjMXucW3gdDk5UkSE9MUXUqtWttPAqYo7FvOMEOAA2dnS\nbbdJY8fSBAEAPO/zz00jRBMEf0IjBAQ4l0u65x6zO9y999pOAwAIRBMmSAkJtlMAxcMzQkCA+89/\npL17pQ8/tJ0EABCIdu+WVqzg7CD4HxohIIAtWya9+KKUns7mCAAA75g2TerdW6pY0XYSoHhYGgcE\nqP37ze4977wj1a9vOw0AIBC5XGY3UpZewx/RCAEBKC9Puvtu6a67pD//2XYaAECgWrlSOn1auvpq\n20mA4qMRAgLQCy9Ix45Jzz1nOwkAIJC9957ZkCcoyHYSoPg4RwgIMKmpZknct99KoaG20yCQMBa7\nx7WBE508aerM6tXSFVfYTgNwjhDgaL/8YpbETZ5MEwQA8K7PPpPatKEJgv+iEQIChMslDR0q3XGH\nOTMIAABvYpME+DuWxgEBYuJE6Y03pLQ0qXx522kQiBiL3ePawGn27pWioqRdu6TLLrOdBjCKOxZz\njhAQADZulJ56Slq6lCYIAOB9M2ZIt95KEwT/xtI4wM+dPGk2R3j+ealZM9tpAABOkJRkjmgA/BlL\n4wA/99e/ShkZ0qxZbF8K72Isdo9rAyfZts2cG5SVJZVjbRF8CEvjAAdJTpY+/FD67juaIABA6Zgx\nQ7r9dpog+D+WxgF+6sABafBgacoUqUYN22kAAE6RlGSWZAP+jkYI8EMulzR8uHTnnVKXLrbTAACc\n4vvvpcOHpU6dbCcBSo5JTcAPzZghrV8vvfee7SQAACd5/30pPl4qw610BAA2SwD8zO7dUtu20rx5\nUkyM7TRwEsZi97g2cAKXS2rYUPrkE1OHAF9T3LGYfh7wIy6XeS5o+HCaIABA6UpLky69VGrTxnYS\nwDNohAA/MnGitH+/9PTTtpMAAJzmzCYJ7FKKQMHSOMBPbNsmdewoLV4sNW9uOw2ciLHYPa4NAl1O\njhQWJi1ZIjVubDsNUDifWhqXnJysZs2aqXHjxhozZkyh70lNTVV0dLRatmyp2NhYb8YB/FZurnTv\nvdI//kETBHgSdQoomsWLTSNEE4RA4rUZodzcXDVt2lQpKSkKDQ1V+/btlZSUpKioqPz3ZGdnq3Pn\nzpo/f77CwsJ04MAB1axZ89yQ3GmDw730kjRnjrRwoVS2rO00cKpAG4upU0DR/b//J4WHS08+aTsJ\n4J7PzAilp6crMjJSERERCg4OVnx8vGbPnl3gPe+//7569+6tsLAwSSq0uABO9+OP0ujR0uTJNEGA\nJ1GngKLJyzM7xfXqZTsJ4Flea4SysrIUHh6e/3VYWJiysrIKvGfLli06ePCgunTpopiYGE2dOtVb\ncQC/lJcnDR0q/fOfZstSAJ5DnQKKJi1NqlFDatLEdhLAs7x2oGpQEbYUOX36tFavXq0FCxbo2LFj\n6tSpk6666io1ZgEqIMnsEnfqlPTgg7aTAIGHOgUUzaxZUu/etlMAnue1Rig0NFSZmZn5X2dmZuYv\nLTgjPDxcNWvWVIUKFVShQgVdd911Wrt2baEFZuTIkfmfx8bG8sAqAt6uXWYmKDWVJXGwIzU1Vamp\nqbZjeA11Crgwl8s0QnPm2E4CnKukdcprmyXk5OSoadOmWrBggUJCQtShQ4dzHkLdtGmTHnjgAc2f\nP18nT55Ux44dNXPmTDX/w7ZYPIQKp3G5pFtvlaKjpVGjbKcBjEAbi6lTwIWtXi3deae0eTPnB8H3\nFXcs9tqMULly5ZSYmKju3bsrNzdXgwcPVlRUlCZMmCBJSkhIULNmzdSjRw+1bt1aZcqU0dChQ88p\nLoATffCBOTfoww9tJwECF3UKuLAzy+JoghCIOFAV8DG//CK1bCl9/LHUqZPtNMBZjMXucW0QiFwu\nKSpKmjJF6tDBdhrgwnxm+2wAF+evf5XuuIMmCABg18aN0rFjUvv2tpMA3uG1pXEAim/+fGnRImn9\nettJAABON2uWOTuIZXEIVMwIAT7iyBFp2DBpwgSpUiXbaQAATse22Qh0PCME+IhHHpEOHjRrsQFf\nxFjsHtcGgWbbNqlzZykriyMc4D98Ztc4AEWXlibNnMmSOACAb/j4Y+m222iCENhYGgdYduqUNGSI\n9MorUo0attMAAMCyODgDjRBg2QsvSA0amAPrAACwbdcuacsWKTbWdhLAu1gaB1j0ww9SYqK0Zg27\n8gAAfMMnn0i33CIFB9tOAngXM0KAJbm5Zkncs89KYWG20wAAYLAsDk5BIwRYMn68uduWkGA7CQAA\nxs8/S999J3XtajsJ4H0sjQMs2LnTzAQtWyaV4XYEAMBHzJ4t9eghXXqp7SSA9/EtGFDKXC4zC/TX\nv0pNm9pOAwDAWSyLg5Nc8EDV7OxsffPNN8rIyFBQUJAiIiLUqVMnValSpbQyclAdAsrUqdLLL0sr\nV/IgKvyLr47F1CnAM379VYqIMIeoVqpkOw1QfMUdi902QkuWLNHYsWOVkZGh6OhohYSEyOVyac+e\nPVqzZo0iIiL097//Xddcc43HwrsNSYFBgPj5Z6lVK2nuXCkmxnYaoHh8bSymTgGeNXWqmRH69FPb\nSYCLU9yx2O0zQp988olefvllNW7cuNCf37x5s958881SKTBAoHj4YWnAAJogwBOoU4BnsSwOTnPB\npXG+gDttCASffy498oi0bp1UsaLtNEDxMRa7x7WBvztyRAoNNZv5VK1qOw1wcYo7Fl9ws4T+/fsr\nOzs7/+uMjAxdf/31F5cOcKhDh6Thw6WJE2mCAE+jTgElN2+e1KkTTRCc5YKN0LXXXquOHTtq7ty5\nmjhxorp166ZHH320NLIBAePJJ6Vu3SS+NwM8jzoFlNzHH7MsDs5TpKVxS5Ys0fXXX6+aNWtq9erV\nqlevXmlky8eSA/izJUuk+Hhp/XqpWjXbaYCL58tjMXUKuHgnTkh160qbN0u1a9tOA1w8jy+Nmzp1\nqgYNGqQpU6bo3nvvVc+ePfXdd9+VKCTgFCdOSEOGSOPG0QQB3kKdAkrmyy+ltm1pguA8F5wRuu22\n2zRx4kTV/t//jvT0dN13332lWmS40wZ/9fTT0qZNZicewN/56lhMnQJK5t57pXbtpAcftJ0EKBmP\nnSN0PidPnlT58uWL+8suGgUG/mjtWqlrV/OxlFfpAF7hT2MxdQoomtOnzbK4devMrnGAP/PY0riR\nI0dq3759hf5c+fLltWfPHo0YMaL4CQEHyMmRBg+WRo+mCQK8hToFlNzChVKTJjRBcCa3B6q2b99e\n8fHxOnXqlK688krVq1dPLpdLe/fu1erVq1W+fHn97W9/K82sgN949VWzBenAgbaTAIGLOgWU3Mcf\nS7162U4B2OF2adzdd9+tqVOn6rnnnlPjxo2VkZGhoKAg1a9fX507d1ZYWFjphWTJAfzItm1Sx45S\nerrUsKHtNIDn+NpYTJ0CSiY318wELV9OvUJgKO5Y7HZGaNWqVdq9e7c++OADpaamFvhNg4KCSpYS\nCFAul3TffdI//kFRAbyNOgWUzLJlZvk29QpO5bYRGjZsmG644QZt375d7dq1K/BzQUFB2r59u9fD\nAf7m3XelQ4ekhx+2nQQIfNQpoGRmzWJZHJztgrvGDRs2TG+++WZp5SkUSw7gD/bskdq0kVJSpNat\nbacBPM9Xx2LqFFB8LpdUv76UnCw1b247DeAZpbJ9dmmjwMDXuVzmrlqLFtJzz9lOA3gHY7F7XBv4\nmxUrzPlBGzfaTgJ4jseeEQJQdB99ZA5OnTHDdhIAAC5s1iypTx/bKQC7mBECSuiXX6SWLc0WpJ06\n2U4DeA9jsXtcG/gTl0tq1MjUrbZtbacBPMdjB6oCKJpHH5XuvJMmCADgH777TipTxjzXCjgZS+OA\nEvjiC2npUmndOttJAAAomo8+Msvi2GUeTseMEHCRDh+Whg2TJk6UKlWynQYAgAtzuUwj1Lu37SSA\nfTRCwEV68knpxhvNCwAAf/DDD9KJE1JMjO0kgH0sjQMuwpIl0qefSuvX204CAEDRnZkNYlkc4OUZ\noeTkZDVr1kyNGzfWmDFj3L5v5cqVKleunD7++GNvxgE84vhxafBgafx4qVo122kAlAR1Ck5z5vkg\nAF5shHJzc/XAAw8oOTlZGzZsUFJSkjYWcmpXbm6unnjiCfXo0YOtR+EXRo0y243edpvtJABKgjoF\np9m0Sfr1V+mqq2wnAXyD1xqh9PR0RUZGKiIiQsHBwYqPj9fs2bPPed+4cePUp08f1apVy1tRAI9Z\ntUqaNEkaN852EgAlRZ2C08yaJfXqZbbOBuDFRigrK0vh4eH5X4eFhSkrK+uc98yePVv333+/JHMI\nEuCrTp0yS+JeekmqU8d2GgAlRZ2C08yaxW5xwO95rREqSrF45JFHNHr06PxTYFlyAF/2/PNSaKjU\nv7/tJAA8gToFJ9m2TcrKkq691nYSwHd4bde40NBQZWZm5n+dmZmpsLCwAu9ZtWqV4uPjJUkHDhzQ\nF198oeDgYMXFxZ3z+40cOTL/89jYWMXGxnolN1CY1aul//7XnMbNDWE4RWpqqlJTU23H8BrqFJxk\n1izzbGvZsraTAJ5T0joV5PLS7a2cnBw1bdpUCxYsUEhIiDp06KCkpCRFRUUV+v6BAwfqlltuUa9e\nvc4N+b87cYANJ09K7dqZc4OYDYKTBdpYTJ2Ck3TsKD33nNS1q+0kgPcUdyz22oxQuXLllJiYqO7d\nuys3N1eDBw9WVFSUJkyYIElKSEjw1h8NeNSoUVLjxlK/fraTAPAk6hScYscOaft2iUlKoCCvzQh5\nEnfaYMuKFdKtt0pr17JBAsBY7B7XBr5s9Ghp507pjTdsJwG8q7hjMRsoAm4cPy7de6/0+us0QQAA\n/zVjhvS/R90A/A6NEODGM89IrVtLd9xhOwkAABdn40Zp/37pmmtsJwF8j9eeEQL82dKl0vvvS+vW\n2U4CAMDFmznT3NBjtzjgXMwIAX9w9Kg0cKA0frxUs6btNAAAXByXi2VxwPnQCAF/8NhjUqdO0l/+\nYjsJAAAXb+1acwREhw62kwC+iaVxwO989pk0f74pHgAA+LMzs0EcBA4Uju2zgf/Zt09q21b64APp\n2mttpwF8D2Oxe1wb+BqXS2rQQJozx2z8AzgB22cDF8HlkgYNMi+aIACAv1uxQqpYUWrVynYSwHfR\nCAGS3nzTzAiNGGE7CQAAJZeUxLI44EJYGgfH27TJnK+wdKnUrJntNIDvYix2j2sDX5KTI4WHS4sW\nSU2a2E5m7klEAAAVpUlEQVQDlB6WxgHFcOqU1K+f9NxzNEEAgMDw1VdS/fo0QcCF0AjB0Z55RqpX\nT0pIsJ0EAADPmDJFGjDAdgrA97E0Do6VnCwNGSKtWSPVqmU7DeD7GIvd49rAVxw6JF1xhbRtm1Sj\nhu00QOkq7ljMOUJwpN27pYEDzRkLNEEAgEDx0UfS9dfTBAFFwdI4OE5urtS/vzRsmPSnP9lOAwCA\n57AsDig6lsbBcZ59Vlq4UEpJkcqWtZ0G8B+Mxe5xbeALMjKkmBiz6uGSS2ynAUofS+OA81i0SHrj\nDWnVKpogAEBgmTZNuvNOmiCgqGiE4Bj795slcZMmSSEhttMAAOA5LpdZFjd1qu0kgP/gGSE4Qm6u\nOS+oXz+pRw/baQAA8KylS81Khw4dbCcB/AeNEBxhxAhz0vZzz9lOAgCA5731ljR0qBQUZDsJ4D/Y\nLAEBb84c6YEHpG+/lWrXtp0G8F+Mxe5xbWDTr79KDRpIW7dKNWvaTgPYw2YJwO9s2WIOTZ0zhyYI\nABCYpk83y75pgoDiYWkcAtbRo1Lv3tKoUdJVV9lOAwCA57lcZlnckCG2kwD+h6VxCEgul3T33ebB\n0cmTWTMNeAJjsXtcG9iycqXZMnvrVqkMt7fhcCyNAyS99JL0ww/SsmU0QQCAwHVmNogmCCg+ZoQQ\ncD7/XEpIkNLSpPBw22mAwMFY7B7XBjYcOWLq3IYNUr16ttMA9jEjBEdbv14aOFD67DOaIABAYJs6\nVerShSYIuFg0QggYBw5IcXHSf/7D5ggAgMDmckmJieYF4OKwohQB4dQpqU8f6Y47zCYJAAAEsq+/\nNs8FxcbaTgL4Lxoh+D2XSxo+XKpcWXr+edtpAADwvnHjzGHhbAgEXDw2S4Df+/e/pU8/lVJTpcsv\nt50GCFyMxe5xbVCaduyQYmKkn36SLrvMdhrAd7BZAhxl8mTp3Xelb76hCQIAOMN//2s2BqIJAkqG\nGSH4rfnzpQEDpEWLpGbNbKcBAh9jsXtcG5SWo0el+vWl9HSpYUPbaQDfwowQHGHNGrMpwscf0wQB\nAJzjnXekP/2JJgjwBBoh+J2tW6U//9ksDbjmGttpAAAoHadPSy+/LH34oe0kQGBg1zj4lV27pK5d\npX/9y2yXDQCAU8ycaWaCOnSwnQQIDF5vhJKTk9WsWTM1btxYY8aMOefnp0+frjZt2qh169bq3Lmz\n1q1b5+1I8FM//2yaoOHDpYQE22kABArqFPyByyWNGSM98YTtJEDg8OrSuNzcXD3wwANKSUlRaGio\n2rdvr7i4OEVFReW/p2HDhlq8eLGqVKmi5ORk3XfffUpLS/NmLPih7Gype3czC/T447bTAAgU1Cn4\ni3nzpLJlTS0E4BlenRFKT09XZGSkIiIiFBwcrPj4eM2ePbvAezp16qQqVapIkjp27Khdu3Z5MxL8\n0JEj0s03S9ddJz37rO00AAIJdQr+4sxsEAeoAp7j1UYoKytL4eHh+V+HhYUpKyvL7fvfeecd9ezZ\n05uR4GcOH5Z69pSioqRXXqEAAPAs6hT8wcKF0p490u23204CBBavLo0LKsZ3rQsXLtS7776rZcuW\nFfrzI0eOzP88NjZWsbGxJUwHX3fokHTTTVKLFtKbb0pl2NoDKFWpqalKTU21HcOrqFPwdS6X2SBo\nxAipHHv9AgWUtE559b9UaGioMjMz87/OzMxUWFjYOe9bt26dhg4dquTkZFWrVq3Q3+v3BQaB77ff\npB49pOhoKTGRJgiw4Y/fzI8aNcpeGC+hTsHXpaRI+/dLffvaTgL4npLWKa9+exkTE6MtW7YoIyND\np06d0syZMxUXF1fgPT/99JN69eqladOmKTIy0ptx4Ceys6Vu3aR27aTx42mCAHgPdQq+7Mxs0MiR\nZqMEAJ7l1RmhcuXKKTExUd27d1dubq4GDx6sqKgoTZgwQZKUkJCgZ599Vr/++qvuv/9+SVJwcLDS\n09O9GQs+bO9eMxMUG8szQQC8jzoFXzZvnnlWlmeDAO8IcrlcLtshLiQoKEh+EBMltG2bmQm6917p\nn/+kCQJ8DWOxe1wbeFpOjtSmjfT889Ktt9pOA/iH4o7FPHYHn7B2rdkd7plnpGHDbKcBAMCuSZOk\nWrWkP6zUBOBBzAjBusWLzbR/YiLT/4AvYyx2j2sDTzpyRGrSRJozR4qJsZ0G8B/FHYt5DB1WTZsm\n9ekjTZ9OEwQAgCSNHStdfz1NEOBtLI2DFXl55kyEadPMQXEtWthOBACAfTt2mB1TV62ynQQIfDRC\nKHXHj5sNEXbtklaskGrXtp0IAADf8PDD0l//KtWvbzsJEPhYGodStWuX2Rq7XDlpwQKaIAAAzpgz\nR9q8WXrsMdtJAGegEUKp+fprqX176S9/MUviLr3UdiIAAHzD0aPSQw+ZZXHly9tOAzgDu8bB61wu\nacwY6bXXTAN0ww22EwG4GIzF7nFtUFKPPSbt2SO9/77tJID/4hwh+JTsbGngQDO4r1wphYXZTgQA\ngG9ZutQ0QN9/bzsJ4CwsjYPXLF5sTsUOD5cWLaIJAgDgj44eNTcM33hDqlnTdhrAWVgaB487fVoa\nNUp65x3p7belm2+2nQiAJzAWu8e1wcV68EGzemLqVNtJAP/H0jhYtWWL1L+/VKOG9N13Up06thMB\nAOCb5swxr+++s50EcCaWxsEjcnKkl16SOnWS+vWT5s6lCQIAwJ2dO6WhQ6UZM6Rq1WynAZyJGSGU\n2Pr10qBBUqVK5oDURo1sJwIAwHedPi3Fx0t/+5u5gQjADmaEcNGOH5dGjpS6dDF3tRYsoAkCAOBC\nHn3ULCHn4FTALmaEUGwul1nT/OijUrt20po17AgHAEBRvPGGuXGYliaV4XY0YBWNEIpl82bp4Yel\njAxp4kTpxhttJwIAwD8sWGBWUixbJlWpYjsNAO5FoEj27zcN0NVXm+Zn7VqaIAAAimrtWqlvX7M5\nQmSk7TQAJBohXMCRI9Kzz0pRUWZJ3IYNZk3zJZfYTgYAgH/YskW66SYpMdE8VwvAN9AIoVDHj0uv\nvy41biz9+KOUnm6+rl3bdjIAAPxHZqbUrZs5aPyOO2ynAfB7PCOEAg4fNg9yvvKK1LGjNG+eFB1t\nOxUAAP5n+3azjPyhh8zuqgB8C40QJEkHDkjjx5tp+65dpS+/lFq1sp0KAAD/tGmTqaf/+Ic0fLjt\nNAAKw9I4h1u3ThoyxCyB++kns5PN++/TBAEAcLGWLTPPAv373zRBgC9jRsiBcnKkzz6TXntN2rrV\nDNKbN0u1atlOBgCAf5s+3ZyzN2WK1KOH7TQAzodGyEF+/FGaNMkMzg0amDXLvXpJwcG2kwEA4N9O\nn5aeekr68EPp66+lli1tJwJwITRCAS47W/roI9MAbd8uDRhgDnSLirKdDACAwLBzpxQfL9WoIX37\nrVSzpu1EAIqCZ4QC0G+/SVOnSrfcItWvb3Z+e/JJ8wzQmDE0QQAAeILLJU2bJnXoIPXuLc2ZQxME\n+BNmhALEzz9LX3whffyxtHChFBtr7k5Nny5Vrmw7HQAAgeWnn6Rhw6SsLHPDsV0724kAFFeQy+Vy\n2Q5xIUFBQfKDmKUqL09as0aaO9e8Nm2SbrhBuvVW86pa1XZCAIGGsdg9ro1zHD9uztr7z3/Mpgh/\n/zvP2gK+orhjMTNCfsLlknbsMLM9qanmOZ/LL5duvll6/nnp2mulSy6xnRIAgMCUkyMlJUlPP20O\nHF+xQmrUyHYqACXBjJCPysuTtmyRli8/2/zk5JhzCWJjzcfISNspATiJE8fiouLaBK5Tp8xuq6NH\nSyEh5ubjNdfYTgWgMMUdi2mEfMT+/VJ6urnDtGKFtHKlebanU6ezjU/jxlJQkO2kAJzKCWPxxeLa\nBJ6sLOmdd6S33pJatDAzQddeazsVgPOhEfJxubnmENN1686+1q4121y3b2+m2zt2NDvQ1KljOy0A\nnBVIY7GncW0Cw8mT0pdfSu++Ky1aJN15p5SQILVtazsZgKKgEfIRx46ZhmfLFmnzZvNav17asEGq\nV09q3dq8WrUyr8hIqQybmQPwYf44FpcWro3/OnbMHID64YfSZ5+Zg1D795fuukuqVMl2OgDFQSNU\nSvLypL17zSFqP/1kPu7Ycbbx2b9fathQatLEvBo3NoNrixZmkwMA8De+OBb7Cq6N/8jNlb7/Xvrq\nKzP7k5YmXXml1KePOQsoJMR2QgAXy6caoeTkZD3yyCPKzc3VkCFD9MQTT5zznoceekhffPGFKlas\nqMmTJys6OvrckKVcYI4eNU3OH1+ZmWcbn127pGrVpCuuMIeWXnGFFBFxtvG54gqpbNlSiwwAXheI\n3+z7a51C0bhc0p490rffmoYnLc18Xq+edOONUrdu5hlcztsDAoPPbJ+dm5urBx54QCkpKQoNDVX7\n9u0VFxenqKio/PfMmzdPW7du1ZYtW7RixQrdf//9SktL82iOkyelgwfP/9q/3zQ6+/aZjzk5ZpCs\nW9c8p3Pm43XXnW18wsOlSy/1aNSLkpqaqtjYWNsxfBLXxj2ujXtcG+fwlToV6Erj/9SJE+ZGZUaG\nOVfvhx/Ma8MGc8bPlVdKV10lPf64eQa3Rg2vxikyxhv3uDbucW08x2uNUHp6uiIjIxURESFJio+P\n1+zZswsUmDlz5uiee+6RJHXs2FHZ2dnat2+f6hSyS8CXX0qHDxf9deiQaXJycqTq1d2/wsLMgFi3\n7tnX5Zf7z+5s/Gdwj2vjHtfGPa6Nc3i6TqFwJfk/dfKkuVm5b5/0888FP+7efXZZ+sGD5gZl/fpS\n06ZSmzbmGZ8WLaRatTz79/Ekxhv3uDbucW08x2uNUFZWlsLDw/O/DgsL04oVKy74nl27dhVaYMaO\nNQ3KH18hIYX/eOXKpsGpWNF/mhoAQOnxdJ1ygrw884xNTo55/f7znBxz5s7x42aG5szHzZvNRgQn\nThT88ePHzU3L334zr8I+P3XKNDK1a5uVGWc+1qsnRUdLDRqYZel167IcHUDxea0RCipi9/HHdXzu\nft1XX5U4EgAA+Txdp3r0MM+kmF9z9lWcr2392tzc8zc4Z752uaRy5cyrbNmCn5cta5aMX3qpVKHC\n2c8zM01D88cfr1DBNDRNm0pVqphX5coFP69UiR1VAXiP1xqh0NBQZWZm5n+dmZmpsLCw875n165d\nCg0NPef3atSoUZELlhONGjXKdgSfxbVxj2vjHtemcI0aNbIdwaM8Xafmz3dGnTrTHBXHli38n3KH\n8cY9ro17XJvCFbdOea0RiomJ0ZYtW5SRkaGQkBDNnDlTSUlJBd4TFxenxMRExcfHKy0tTVWrVi10\nucHWrVu9FRMA4FDUKQBwNq81QuXKlVNiYqK6d++u3NxcDR48WFFRUZowYYIkKSEhQT179tS8efMU\nGRmpyy67TJMmTfJWHAAACqBOAYCz+cWBqgAAAADgST79CGJycrKaNWumxo0ba8yYMbbj+JTMzEx1\n6dJFLVq0UMuWLfX666/bjuRTcnNzFR0drVtuucV2FJ+TnZ2tPn36KCoqSs2bN+dMlN954YUX1KJF\nC7Vq1Up33XWXTp48aTuSNYMGDVKdOnXUqlWr/B87ePCgunbtqiZNmqhbt27Kzs62mNB3UKsKR506\nP+qUe9Qp96hTZ3miTvlsI3TmoLvk5GRt2LBBSUlJ2rhxo+1YPiM4OFivvPKKfvjhB6WlpWn8+PFc\nn9957bXX1Lx5czbZKMTDDz+snj17auPGjVq3bl2BM1OcLCMjQ2+99ZZWr16t77//Xrm5uZoxY4bt\nWNYMHDhQycnJBX5s9OjR6tq1qzZv3qwbbrhBo0ePtpTOd1Cr3KNOnR91yj3qVOGoUwV5ok75bCP0\n+4PugoOD8w+6g1G3bl21bdtWklSpUiVFRUVp9+7dllP5hl27dmnevHkaMmTIOdveOt1vv/2mJUuW\naNCgQZLMMxJVqlSxnMo3VK5cWcHBwTp27JhycnJ07NixQncHc4prr71W1apVK/Bjvz9c9J577tGn\nn35qI5pPoVa5R51yjzrlHnXKPepUQZ6oUz7bCBV2iF1WVpbFRL4rIyNDa9asUceOHW1H8QmPPvqo\nxo4dqzIcPnGOHTt2qFatWho4cKCuvPJKDR06VMeOHbMdyydUr15djz32mK644gqFhISoatWquvHG\nG23H8in79u3L3zGtTp062rdvn+VE9lGrioY6VRB1yj3qlHvUqQsrbp3y2f+BTBUXzZEjR9SnTx+9\n9tprqlSpku041n3++eeqXbu2oqOjuctWiJycHK1evVrDhw/X6tWrddlll7G86X+2bdumV199VRkZ\nGdq9e7eOHDmi6dOn247ls4KCghinRa0qCupUQdSp86NOuUedKp6i1CmfbYSKctCd050+fVq9e/dW\n//79ddttt9mO4xOWL1+uOXPmqEGDBurbt6++/vprDRgwwHYsnxEWFqawsDC1b99ektSnTx+tXr3a\ncirf8O233+rqq69WjRo1VK5cOfXq1UvLly+3Hcun1KlTR3v37pUk7dmzR7Vr17acyD5q1flRp85F\nnTo/6pR71KkLK26d8tlG6PcH3Z06dUozZ85UXFyc7Vg+w+VyafDgwWrevLkeeeQR23F8xvPPP6/M\nzEzt2LFDM2bM0PXXX68pU6bYjuUz6tatq/DwcG3evFmSlJKSohYtWlhO5RuaNWumtLQ0HT9+XC6X\nSykpKWrevLntWD4lLi5O7733niTpvffe4xtbUavOhzpVOOrU+VGn3KNOXVhx65TXDlQtKXcH3cFY\ntmyZpk2bptatWys6OlqS2VKxR48elpP5FpatnGvcuHHq16+fTp06pUaNGnFA5P+0adNGAwYMUExM\njMqUKaMrr7xS9913n+1Y1vTt21eLFi3SgQMHFB4ermeffVZPPvmk7rjjDr3zzjuKiIjQBx98YDum\nddQq96hTRUOdOhd1qnDUqYI8Uac4UBUAAACA4/js0jgAAAAA8BYaIQAAAACOQyMEAAAAwHFohAAA\nAAA4Do0QAAAAAMehEQIAAADgODRCAAAAAByHRggAAACA49AIAV60cuVKtWnTRidPntTRo0fVsmVL\nbdiwwXYsAAAkUafgbEEul8tlOwQQyJ555hmdOHFCx48fV3h4uJ544gnbkQAAyEedglPRCAFedvr0\nacXExKhChQr65ptvFBQUZDsSAAD5qFNwKpbGAV524MABHT16VEeOHNHx48dtxwEAoADqFJyKGSHA\ny+Li4nTXXXdp+/bt2rNnj8aNG2c7EgAA+ahTcKpytgMAgWzKlCkqX7684uPjlZeXp6uvvlqpqamK\njY21HQ0AAOoUHI0ZIQAAAACOwzNCAAAAAByHRggAAACA49AIAQAAAHAcGiEAAAAAjkMjBAAAAMBx\naIQAAAAAOA6NEAAAAADHoRECAAAA4Dj/H+CbMpJydnt4AAAAAElFTkSuQmCC\n",
       "text": "<matplotlib.figure.Figure at 0x7f7096bb0b90>"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## Building the Bayesian Model"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import pymc as pm\nimport random\nimport math\n\n# Some artificial data\n# The learner will answer correctly 70% of the time\ndata = []\nfor i in xrange(500):\n    x = random.random()\n    if (x > 0.3):\n        data.append(1)\n    else:\n        data.append(0)\n\na = 1\nb = 1\n        \n# Define theta with a uniform distribution\ntheta = pm.Beta('theta', a, b)\n\n# p is obtained from a logistic function of theta and a\n@pm.deterministic\ndef p(theta=theta):\n    return 1.0 / (1 + math.exp(-1 * (theta * 10 - 5)))\n\n# x is observed data, it is drawn from a Bernoulli distribution,\n# with parameter p, i.e. P(x=1) = p\n# 'data' contains observed data defined above, and we set observed=True\nx = pm.Bernoulli('x', p, value=data, observed=True)\n#x = pm.Binomial('x', n=len(data), p=p, value=data.count(1), observed=True)\n\n# Define a pymc model with all the components\nmodel = pm.Model([theta, p, x])\n",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## Obtaining the MAP (Maximum a Posterior Probability)"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# Create a MAP (maximum a posteriori estimate) object\nm = pm.MAP(model)\nm.fit()\n\n# Check the MAP estimate of the variables\nprint \"Theta: %.4f\" % m.get_node('theta').value\nprint \"p    : %.4f\" % m.get_node('p').value\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "Theta: 0.5847\np    : 0.7000\n"
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## Using MCMC to Obtain Samples from Posterior Distributions"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# from the posterior probability distributions\nmcmc = pm.MCMC(model)\nmcmc.sample(iter=5000, burn=1000)\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\r [-----------------95%----------------  ] 4778 of 5000 complete in 0.5 sec"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\r [-----------------100%-----------------] 5000 of 5000 complete in 0.5 sec"
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "plt.figure(figsize=(16,4))\n\nplt.subplot(1, 2, 1)\nplt.hist(theta.trace(), bins=np.linspace(0, 1, 100), facecolor=\"#88AAFF\")\nplt.xlim((0,1))\nplt.title('theta')\n\nplt.subplot(1, 2, 2)\nplt.hist(p.trace(), bins=np.linspace(0, 1, 100), facecolor=\"#88AAFF\")\nplt.xlim((0,1))\nplt.title('p')\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": "<matplotlib.text.Text at 0x7f7083835e10>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA60AAAEKCAYAAAD5I7OgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": "<matplotlib.figure.Figure at 0x7f708368e510>"
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}